Question

Solve 6x + 3y = 6xy, 2x + 4y = 5xy.

Answer 1

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Answer 2

Answer:

x = 1 , y = 2

Solution:

Given pair of equations are :

6x + 3y = 6xy --------(1)

2x + 4y = 5xy -------(2)

Equation (1) can be written as :

=> 6x + 3y = 6xy

=> 3(2x + y) = 6xy

=> 2x + y = 2xy

=> 2x/xy + y/xy = 2

=> 2/y + 1/x = 2

=> 1/x + 2/y = 2 --------(3)

Equation (2) can be written as ;

=> 2x + 4y = 5xy

=> 2x/xy + 4y/xy = 5

=> 2/y + 4/x = 5

=> 4/x + 2/y = 5 ---------(4)

Putting 1/x = a and 1/y = b in eq-(3) and (4) ,we get;

a + 2b = 2 ------(5)

4a + 2b = 5 -------(6)

Now,

Subtracting eq-(5) from (6) , we get ;

=> (4a + 2b) - (a + 2b) = 5 - 2

=> 4a + 2b - a - 2b = 3

=> 3a = 3

=> a = 3/3

=> a = 1

=> 1/x = 1

=> x = 1

Now,

Putting a = 1 in eq-(5) , we get ;

=> a + 2b = 2

=> 1 + 2b = 2

=> 2b = 2-1

=> 2b = 1

=> b = 1/2

=> 1/y = 1/2

=> y = 2 .

Hence,

The required solution is ; x = 1 , y = 2.